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29/12/04 5x5 magic square program source is now available!! Please view description below.
Do you know Magic Squares?
For example, 4x4 magic square puts in the number of 1-16 into the grid of
4x4,
and the sum total of the numbers perpendicularly, horizontally, and diagonal
located
in line is set to 34.
（The following figure shows an example of 4x4 magic square.）
Moreover, 5x5 magic square puts in the number of 1-25 into
the grid of 5x5,
and the sum total of the numbers perpendicularly, horizontally, and diagonal
located
in line is set to 65.
（The following figure shows an example of 5x5 magic square.）
Moreover, 6x6 magic square puts in the number of 1-36 into
the grid of 6x6,
and the sum total of the numbers perpendicularly, horizontally, and diagonal
located
in line is set to 111.
（The following figure shows an example of 6x6 magic square.）
Since the predecessors have explained how to make for the order of
numbers in many WEB sites,
no related theory is shown here.
The purpose of this page is to introduce some programs that number the total of 4x4 , 5x5 and 6x6 magic squares.
The total of magic squares is the number of the orders that satisfy the sum
of 4 , 5 or 6 numbers located in line,
but exclude what is made right and left reversed, upside down
exchanged, or rotated 180 degrees.
<A program to number
the total of 4x4 magic squares (Windows version)>
<The source code of
program to number the total of 4x4 magic squares (Linux C language version)> New!!
The total of the orders of 4x4 magic square is 880.
<A program to
number the total of 5x5 magic squares (Windows version)>
<A program
to number the total of 5x5 magic squares (Linux version)>
<The source code of
above program (C language version)>
The total of 5x5 magic squares increases in number to 275,305,224 at a
stretch.
Since it is a serious number, it takes
time considerably also with the latest personal computer.
Then, although 4 numbers except the center on a diagonal line have 12
kinds of order in a line, it is enabled
to calculate 1/4 of the total using a rule of what 12 kinds are made of 4
times of 3 basic orders.
Even if counting quarter of the total, it requires time too much.
Then, the above programs are enabled to count the total for each number
of the center of 5x5 grid.
(center) (sub total) (quarter sub total) 1 4,365,792 1,091,448 2 5,464,716 1,366,179 3 7,659,936 1,914,984 4 7,835,348 1,958,837 5 9,727,224 2,431,806 6 10,403,516 2,600,879 7 12,067,524 3,016,881 8 12,448,644 3,112,161 9 13,890,160 3,472,540 10 13,376,136 3,344,034 11 15,735,272 3,933,818 12 15,138,472 3,784,618 13 19,079,744 4,769,936 14 15,138,472 3,784,618 15 15,735,272 3,933,818 16 13,376,136 3,344,034 17 13,890,160 3,472,540 18 12,448,644 3,112,161 19 12,067,524 3,016,881 20 10,403,516 2,600,879 21 9,727,224 2,431,806 22 7,835,348 1,958,837 23 7,659,936 1,914,984 24 5,464,716 1,366,179 25 4,365,792 1,091,448 Total 275,305,224 68,826,306(Usage of the Windows version <msq5e.exe>)
The total of 6x6 magic square is not decided although a report
is told that there is near 1,800 trillion order.
<A program to
number the total of 6x6 magic squares (Windows version)> New!!
Even if Pentium4 machine working at 3GHz is used, it is thought that it will
take 220,500 years or more by the time
the above program is finished. Therefore, please use moderately.
>> The Windows version program above-mentioned was created by Borland C++ Builder 6. Moreover, the Linux version was compiled by gcc-3.2.2-5. >> Although the above-mentioned program is freeware, Netstaff Co.,Inc. owns copyright. If it is not the profit purpose, use freely. >> Those who wish to reproduce need to inform by Mail. [Exemption from responsibility] Also what damage after using the above-mentioned program, Netstaff Co.,Inc. takes no responsibility. |
